Question

Which term of the AP 121, 117, 113, ... is its first negative term?

Answer 1

The given AP is 121, 117, 113, ... .

Here, a = 121 and d = 117 − 121 = −4

Let the n^th term of the given AP be the first negative term. Then,

$$\begin{gathered} a_n<0 \\ \Rightarrow 121+\left(n-1\right)\times \left(-4\right)<0\left[a_n=a+\left(n-1\right)d\right] \\ \Rightarrow 125-4n<0 \\ \Rightarrow -4n<-125 \end{gathered}$$
$$\begin{gathered} \Rightarrow n>\frac{125}{4}=31\frac{1}{4} \\ \therefore n=32 \end{gathered}$$

Hence, the 32nd term is the first negative term of the given AP.